Earlier quoted context omitted.
The most effective way is to take notes on a pad or a spiral notebook. Eventually, run them through a scanner. (How are you going to enter equations, draw arrows and diagrams, etc., with a keyboard? If you have a stylus "works almost as good as a pen!", just use a pen on paper. Yes, I'm old, and I wear a watch, too.)
This is a fascinating challenge. I feel like it's probably possible to enter and edit equations as easily with the keyboard as with a pen; certainly you can do so for numerical expressions, using RPN. I wrote a quick hack at http://canonical.org/~kragen/sw/dev3/rpn-edit#3_1_7_1_15_1_1... that almost does a reasonable job; I think that, although it doesn't quite reach being a usable equation editor, among other things…
Besides, my spiral notebook's battery never gives out, it's light, it's $.79, nobody is going to steal it, it doesn't make any noise, it doesn't distract anyone behind me, it won't break when I drop it, etc. Besides, no notes are complete unless you have a coffee cup ring on it.
Disco is music's greatest achievement, too.